Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Elastoresistivity of TTF-TCNQ and related compounds

Elastoresistances of TCNQ high conducting salts have been measured at room temperature by an original strain gauge technique. The effects, on the longitudinal and transverse resistivities ?, of an elementary uniaxial strain ? applied along one of the three axes, a, b or c¹ respectively, have been estimated.For TTF-TCNQ, they are:

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{a}}\text{=? ln ?}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{a}}\text{= 16±3}$

;

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{b}}\text{= ? ln α}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{b}}\text{= 34±4}$

;

(5% risk).So, in an hydrostatic pressure experiment, the fraction of piezoresistivity attributable to transverse effects is 43± 10% of the total value χ^b (K^b_a and K^b_c effects accumulated).Low values have been found for the anisotropy (?^a/?^b) variations due to strains. So one may write:

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{a}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{a}}\text{≌K}{}^{\mathrm{a}}{}_{\mathrm{b}}$

;

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{b}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{b}}\text{≌ K}{}^{\mathrm{b}}{}_{\mathrm{b}}$

;

.The TTF-, HMTTF-, TSF-, HMTSF-TCNQ elastoresistance values are coherent with the previously measured hydrostatic pressure piezoresistivity values.All these experimental results are in good agreement with a model where the longitudinal but also the transverse elastoresistivities are essentially due to variations with strains of the longitudinal scattering time τ_ν defined by σ^b = ne²τ_ν/m¹.     

Investigation of the central component of SrTiO3 by neutron scattering with eV resolution

We studied the energy width and the width in reciprocal space Δq of the central mode of SrTiO₃ above T_c. At T_c+4° we observed an energy width of about 6×10^?7 eV. If the measured Δq is interpreted by a correlation length $\text{Δq}{}^{\mathrm{?1}}\text{= ξ = ξ}{}_0\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>2</mtext><mtext>3</mtext>}}$ we obtain $\text{ξ}{}_0\text{= 75}\text{A}\text{?}$.     

Complexified Pöschl–Teller II potential model

With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Pöschl–Teller II potential, , where q_c=q₀e^2iαε, real V₁>0, q₀>0 and $\text{0<λε<}\text{π}\text{2}$. It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as $\text{PxP}{}^{\mathrm{-1}}\text{=}\text{ln}\text{q}{}_0\text{λ}\text{−x}$. The discrete energy eigenvalues are shown to be real when $\text{V}{}_2\text{⩾−}\text{q}{}_0\text{λ}{}^2\text{4}$ while they are complex conjugate pairs if $\text{V}{}_2\text{<−}\text{q}{}_0\text{λ}{}^2\text{4}$.     

The phase transition at −41°C in Cu4SnS4 as observed in electron microscopy

Evidence, by means of electron microscopy and diffraction, is presented for a phase transformation at around 232 K in Cu₄SnS₄. A superlattice is observed along $\text{q}{}_{\mathrm{1,2}}\text{= ±}\text{1}\text{2}\text{b}{}^1\text{+}\text{1}\text{2}\text{c}{}^1$, presumably associated with a displacive transformation. The first order transformation is associated with a space group change. Satellite dark field imaging revealed a domain structure composed of orientation and translation interfaces.     

Reflection of long waves by interfaces

We derive comparison identities for waves satisfying the equation d²Ψ/dz²+q²(z)Ψ=0. One of these identities is used to show that to second order in the product (wavenumber component normal to interface) × (interface thickness), the reflection amplitude is given by $\text{r=(1?2q}{}_1\text{q}{}_2\text{l}{}^2\text{)}\text{(q}{}_1\text{?q}{}_2\text{)}\text{(q}{}_1\text{+q}{}_2\text{)}$, where l is a legnth determined by the deviation of the interface profile from a step, and q₁, q₂ are the normal components of the wave numbers in media 1 and 2 on either side of the interface. For the continuous interfaces discussed, l is about two-fifths of the 10–90 interface thickness. The corresponding formula for the transmission amplitude is $\text{t=(1+}\text{1}\text{2}\text{(q}{}_1\text{?q}{}_2\text{)}{}^2\text{l}{}^2\text{)}\text{2q}{}_1\text{(q}{}_1\text{+q}{}_2\text{)}$.     

Stark effect in the torsio-rotational spectrum of propargyl mercaptan and SH bond moment determination

The Stark effect of rotational and torsio-rotational transitions of propargyl mercaptan has been analyzed. Assuming a dependence of the dipole moment components on the internal rotation angle of the type: $\text{μ}{}_{\mathrm{a}}\text{= μ}{}_{\mathrm{a}}{}^0\text{+ μ}{}_{\mathrm{a}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, $\text{μ}{}_{\mathrm{b}}\text{= μ}{}_{\mathrm{b}}{}^0\text{+ μ}{}_{\mathrm{b}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, and $\text{μ}{}_{\mathrm{c}}\text{= μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{sin}\text{α}$, the following values of the determinable quantities were obtained: $\text{μ}{}_{\mathrm{a}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.718 ± 0.003}\text{D}$, $\text{μ}{}_{\mathrm{b}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.495 ± 0.010}\text{D}$, and $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{= 0.809 ± 0.015}\text{D}$.The SH bond moment was also evaluated from $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}$ and compared with the SH bond moment of similar molecules.     

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase (h?h_ch_c), $\text{χ ～ (h?h}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{In}{}^{\mathrm{<mtext>-4</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h?h}{}_{\mathrm{c}}$ and R_c ～ (h ? h_c)^{$\text{2}\text{3}$}. In${}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h ? h}{}_{\mathrm{c}}$. Far from commensurability $\text{(h?h}{}_{\mathrm{c}}\text{) χ～ (a+h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, $\text{R}{}_{\mathrm{c}}\text{～ (a + h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.     

Charge density wave commensurability in 2H-TaS2 and AgxTaS2

The charge density wave transition in 2H-TaS₂near 75 K has been observed to be incommensurate, using electron diffraction, with $\text{q}{}^1\text{= (}\text{0.338}\text{±}\text{0.002}\text{)a}{}^1{}_0$ along the 〈10.0〉 directions which, within the experimental uncertainty, remains temperature independent to about 14 K. Incommensurate charge density formation is also observed in Ag_xTaS₂ samples for $\text{x?}\text{0.26}$ with an increase in q¹ to $\text{(}\text{0.347}\text{±}\text{0.002}\text{)a}{}^1{}_0$ when x?0.26. Within the experimental error q¹ appears to be temperature independent to 25 K.     

Light-cone expansions,the parton model and virtual γγ scattering

It is shown that it is sufficient to use the light-cone algebra of currents and the algebra of bilocal operators to find the asymptotic behaviour of the γγ scattering amplitude when one (or two) of the photon masses q_1,2² is large, and for an arbitrary value of the energy squared s = (q₁+q₂)². A general form of this asymptotic behaviour is obtained. The box-diagram is dominant over the wide region in $\text{s(μ}{}^2\text{« s « q}{}_1{}^2\text{q}{}_2{}^2\text{/μ}{}^2\text{,μ ～ 1}\text{GeV}\text{)}$ and so the asymptotic amplitude is known completely. It is shown that the parton model of the type of ref.[8] gives the same predictions for the asymptotic behaviour of the γγ amplitude.     

Intensities and pressure-broadened widths of CO2 R-branch lines at 15 μm from tunable laser measurements

Intensities and half-widths of individual lines, over the temperature range 200–325°K in the 15 μm bands of ¹²C¹⁶O₂, have been determined with a tunable diode laser spectrometer. Measurements were made on pure CO₂ and on dilute CO₂-in-N₂ mixtures on the R-branches of the 01¹0-00⁰0 and 02²0-01¹0 transitions. Intensities are approximately equal to those listed in the AFGL compilation. The pressure-broadened half-widths follow the general relationship $\text{b}{}_{\mathrm{L}}{}^0\text{(T) = b}{}_{\mathrm{L}}{}^0\text{(T}{}_0\text{) [}\text{T}{}_0\text{T}\text{]}{}^{\mathrm{n}}$ where n varies considerably from line to line but is always greater than $\text{1}\text{2}$.     

Multiplicity distribution in antiproton-proton interactions

In a compilation of $\text{p}\text{p}$ interactions we present evidence for KNO scaling in the primary momentum region up to 7 GeV/c. The average multiplicity in $\text{p}\text{p}$ interactions and annihilations has a logarithmic increase with energy. The reduced statistical momenta of multiplicity distribution $\text{c}{}_{\mathrm{q}}\text{=}\text{〈n}{}^{\mathrm{q}}\text{〉}\text{〈n〉}{}^{\mathrm{q}}$ are energy independent and for all final states have practically the same values as in proton-proton interactions. In annihilations the c_q to appear to be different from those in pp interactions and the KNO scaling function is also different.     

An experimental study of the form factor in the decay K+ → πoe+ν

The q² variation of the factor $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)}$ in the decay K⁺→π⁰e⁺ν has been studied using a sample of even detected in the CERN 1.1 m³ heavy-liquid bubble chamber. The data are consistent with a linear development $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)=?}{}_{\mathrm{+}}\text{(0) (1+λ}{}_{\mathrm{+}}\text{q/m}{}^2{}_{\mathrm{\pi }}\text{)}$ with λ₊=0.027±0.008.     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

Deep inelastic structure functions of the photon

Three independent structure functions of a real photon can be measured in photon-photon collisions in e^±e^? storage rings. These are M₁ and M_L (related to the usual structure functions W₁andνW₂, as defined for any target) and a third function M₃, which arises from the strong plane polarisation of the colliding photons. We show, using a dispersion relation in the photon mass, that M₃ and the longitudinal structure function M_L both scale and are independent of the vector-dominant hadronic structure of the real photon. Therefore in a parton model, or in the quark light-cone algebra, they are given by the bare quark box diagrams which also dominate when both photons have large q²; this uniquely predicts the behaviour , $\text{M}{}_3\text{= [(}\text{1}\text{2}\text{π)Σ e}{}_{\mathrm{i}}{}^4\text{](?x}{}^2\text{)}$ for the real photon structure functions in the Bjorken limit (q₂² → ?∞, q₁²=0, x=?q₂²/2q₁·q₂=constant).     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.